I was wondering if it's possible to combine buys from different sources? I bought EAW from Steam, but currently the DLC isn't on offer there anymore while it is on AGEOD's webshop. If I bought Breaking The Deadlock from AGEOD directly, would it work with my Steam-version main game?

yes and no. If you install an Ageod DLC on a Steam version, the files will be copied (provided you know where to install them), but as soon as Steam detects a change that is not 'registered', it will try to revert the files to their expected states.